Problem: Simplify the following expression: $ p = \dfrac{1}{-9q + 2} - \dfrac{10}{7} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{1}{-9q + 2} \times \dfrac{7}{7} = \dfrac{7}{-63q + 14} $ Multiply the second expression by $\dfrac{-9q + 2}{-9q + 2}$ $ \dfrac{10}{7} \times \dfrac{-9q + 2}{-9q + 2} = \dfrac{-90q + 20}{-63q + 14} $ Therefore $ p = \dfrac{7}{-63q + 14} - \dfrac{-90q + 20}{-63q + 14} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{7 - (-90q + 20) }{-63q + 14} $ Distribute the negative sign: $p = \dfrac{7 + 90q - 20}{-63q + 14}$ $p = \dfrac{90q - 13}{-63q + 14}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-90q + 13}{63q - 14}$